The first 20 magic constants are:
15 34 65 111 175 260 369 505 671 870 1105 1379 1695 2056 2465 2925 3439 4010 4641 

The 1,000th magic constant is:
503006505

10 ^ 1 => 3 
10 ^ 2 => 6 
10 ^ 3 => 13 
10 ^ 4 => 28 
10 ^ 5 => 59 
10 ^ 6 => 126 
10 ^ 7 => 272 
10 ^ 8 => 585 
10 ^ 9 => 1260 
10 ^ 10 => 2715 
10 ^ 11 => 5849 
10 ^ 12 => 12600 
10 ^ 13 => 27145 
10 ^ 14 => 58481 
10 ^ 15 => 125993 
10 ^ 16 => 271442 
10 ^ 17 => 584804 
10 ^ 18 => 1259922 
10 ^ 19 => 2714418